Planar Amplitudes in Maximally Supersymmetric Yang-Mills Theory

TL;DR

This paper explores the structure of scattering amplitudes in maximally supersymmetric Yang-Mills theory, revealing that higher-loop amplitudes can be expressed in terms of one-loop amplitudes, indicating a simplified all-orders structure.

Contribution

It explicitly demonstrates the relation between two-loop and one-loop four-point amplitudes and conjectures a similar relation for n-point amplitudes in planar N=4 super-Yang-Mills theory.

Findings

Two-loop four-point amplitudes can be expressed in terms of one-loop amplitudes.

A conjecture extends this relation to n-point amplitudes.

The results align with AdS/CFT expectations of amplitude simplicity.

Abstract

The collinear factorization properties of two-loop scattering amplitudes in dimensionally-regulated N=4 super-Yang-Mills theory suggest that, in the planar ('t Hooft) limit, higher-loop contributions can be expressed entirely in terms of one-loop amplitudes. We demonstrate this relation explicitly for the two-loop four-point amplitude and, based on the collinear limits, conjecture an analogous relation for n-point amplitudes. The simplicity of the relation is consistent with intuition based on the AdS/CFT correspondence that the form of the large N_c L-loop amplitudes should be simple enough to allow a resummation to all orders.